I am saying that if two cars are both Fords, then that is an instance of 'identity'. — Wayfarer

Per realists on universals, sure. But denying that they share an identical property isn't denying the principle of identity in general. It's just denying identity for numerically distinct entites. The principle of identity doesn't necessarily refer to identity of numerically distinct entities.

Oh, I get it. This is one of those arguments, where you get to define the meanings of the terms as we go along, as 'meaning is subjective', right? That's neat, because it means you never have to lose an argument, you just put the goalposts where you like, and then kick the ball through it, saying 'I won', right? And when asked for who the paradigmatic philosophers are who exemplify this excellent technique of yours, the answer is, there are none. It serves me right wasting time talking to fools. I will know better next time.

The principle of identity doesn't conventionally necessarily refer to the identity of numerically distinct entities.

If you were under the impression that it did, you didn't understand the conventional sense of the principle of identity.

Not at all - generality is opposed to particularity, and not singularity; the particular is what is replaceable, interchangeable, amenable to generalization, while the singular is not. Singularity (and it's natural 'pairing', universality, which is in turn not generality) cuts across the general-particular dichotomy, such that a general regime may itself be particular. — StreetlightX

This is an important principle, but I prefer to express "singularity" as "unity", or in the old fashioned way, "One". There is an interesting dialectic on this principle near the end of Plato's Parmenides, I believe. It may or may not be decipherable, but the uninterpretability of it may be intentional, actually what makes the point. "One" is demonstrated to dissolve the categorical boundary between universal and particular, and complete confusion ensues.

Let me see if I can remember the basics. Same is opposed to Other. "Other" is the name of the category of particulars, difference being what constitutes other, and this is the determining factor of particulars. Same is the determining factor of universals, so "Same" is the name for the category of universals . Now we introduce the name "One". Each particular is a unit, a one, so each other is itself a unit, and in this way "One" participates in the category of Other, particulars. However, "One" is what "same" refers to, meaning that everything in the category of Same is by this means, one, the same thing. But "one" designates a particular.

There is no apparent way to resolve this. So when we use "one", or "unit" or "singularity", there is no resolution to the question of what is being referred to, a universal (Same), or a particular (Other). And since same and other are opposing terms, we are open to an infinity of possibilities with the name "One".

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It is transparent that you are adopting the tactic of wasting my time by demanding definitions of the obvious. Respond to my original point - that wiki page is all you need.

The One can be pretty much be read as the argument for vagueness or Apeiron as the foundation for dichotomous or dialectical being.

For contrarieties to constitute existence, then there must be some deeper symmetry state that they break. The dialogue makes that (triadic/developmental) argument. For there to be flux and stasis, etc, there must be a "prior" state that is neither yet has the potential to be so divided.

And note that the quandaries presented in Parmenides were resolved in the late Sophist in fully triadic fashion. Both sameness and difference, generality and particularity, have being. Dichotomies are separations towards mutually logical limits and so where there is distinctive being, it is the result of a successful process of division. Being needs the emergence of the two ends that thus bound a concrete spectrum of possibility.

Realists on universals claim that properties are identical instantiations of a separately existing universal like this: [diagram] It's important to note that realists on universals are saying that the instantiations are identical, that is "one and the same," in a complete sense, of the universal at hand. Literally, they're not two separate things, but the same thing somehow multiply instantiated. — Terrapin Station

Reading Paul Forster's book, Peirce and the Threat of Nominalism - thanks to for bringing it to my attention - is helping me to get a better handle on why this presentation did not sit right with me. It might be an accurate description of Platonism, but - as I have pointed out before - there are other forms of realism that do not claim that universals are "separately existing," even while holding them to be real by a different mode of being.

More to the point that we were discussing, it is not necessary for the realist to claim that the instantiations of a universal are numerically identical. Instead, they are different actualizations of the same inexhaustible continuum of possibilities. The nominalist, on the other hand, insists that what we call universals are sets or collections of discrete individuals. This is why Peirce said that "the question of nominalism and realism has taken this shape: Are any continua real?" It also gets at why I was suggesting that space and time would have to be discrete on the nominalist view - each instance of "here and now" has to be an individual.

An entertainingly blunt assessment of this kind of "strict individualism" is www.iupui.edu/~arisbe/menu/library/aboutcsp/o'hara/csp-plato.htm

It talks of how Peirce viewed Plato's take on universals - how the late Plato was foreshadowing the mature Peircean understanding. :)

Thanks, that was indeed a good read.

The One can be pretty much be read as the argument for vagueness or Apeiron as the foundation for dichotomous or dialectical being. — apokrisis

We need to respect what the argument demonstrates though, that the real existence of unity, represented as "One", throws confusion into our understanding of reality, if we maintain the traditional categorical separation of universal/particular. The conclusion to be drawn is not that "One" is some sort of unintelligible vague being or existence, but that our defined categories, particular and universal, are inadequate for understanding the nature of reality.

And note that the quandaries presented in Parmenides were resolved in the late Sophist in fully triadic fashion. Both sameness and difference, generality and particularity, have being. Dichotomies are separations towards mutually logical limits and so where there is distinctive being, it is the result of a successful process of division. Being needs the emergence of the two ends that thus bound a concrete spectrum of possibility. — apokrisis

I think that what is demonstrated in those Platonic dialogues is that this dichotomy, between universal and particular cannot by maintained at the most fundamental level. The world becomes unintelligible at this level, in terms of these two categories, because there is something which violates the boundary between them, something more fundamental.

You'll notice that in the Timaeus, Plato introduces a completely new dichotomy, that of matter and form. "Matter" is a new term, and it has taken the place of the particular, as the possibility of a particular.
Form is what gives actual existence to the particular. This allows Aristotle to develop "form" as a category which includes both particulars and universals. The form of the universal is the essential properties, the form of the particular is the essential properties as well as all the accidentals. From this perspective both universals and particulars are intelligible objects.

Matter itself has been excluded from this category of intelligibility, in order that particulars and universal can both be included, as intelligible. Matter is still very real, as that which bridges the boundary between the possibility of a particular, and the actuality of a particular, but the categories have been redefined, such that particulars can be brought in with universals, as intelligible. The new categories as defined by Aristotle are "actual" and "potential". This validates what you say: "both sameness and difference, generality and particularity, have being", because both are in the category of "actual", as two distinct types forms.

For contrarieties to constitute existence, then there must be some deeper symmetry state that they break. The dialogue makes that (triadic/developmental) argument. For there to be flux and stasis, etc, there must be a "prior" state that is neither yet has the potential to be so divided. — apokrisis

I don't think this "triadic/development" is the right direction. What you propose only reinforces the designated status of matter (potential) as unintelligible. it asserts the position of the unintelligible (matter) as more fundamental than the intelligible, placing it out of reach of the intellect. A more appropriate approach, I believe, is to redefine the categories again, similar to what Plato and Aristotle did, but now to bring matter into the category of intelligibility. Plato and Aristotle made the particular intelligible by providing the principles necessary to bring it into the same category as the universal. Now we need to provide the principles necessary to bring matter into the same category, as that which separates a particular from a universal, within that category. This will bring matter (potential) out from the designation of vagueness, the apeiron, into the category of intelligible.

there are other forms of realism that do not claim that universals are "separately existing," even while holding them to be real by a different mode of being. — aletheist

I just want to do this one step at a time, and I want you to think about this. Don't just defer until you get a chance to read something someone else wrote in order to provide you with an answer:

First, logically, I'd say that we only have two possibilities regarding the presence of properties (where we're accepting or assuming there are properties) with respect to the idea of universals: either (1) the properties are only in (or of) particulars, in which case they're not separately existing, or (2) the properties are (at least partially) separate from particulars and are instantiated in particulars. Or to state that in a less wordy way (though as always that makes it a way more prone to nitpicking): As long as we accept that there are properties and particulars that exhibit properties, there are only two possibilities: there are only properties "in" particulars or there are also properties separate from particulars.

Do you agree with this? Or do you believe that there is at least a third logical possibility? (And if so, what is a third possibility?)

As long as we accept that there are properties and particulars that exhibit properties, there are only two possibilities: there are only properties "in" particulars or there are also properties separate from particulars. — Terrapin Station

I am suggesting that both of these statements are correct, but "there are" means two different things. Properties only exist in particulars, but properties are real - i.e., they have another mode of being - apart from particulars. Each actual property is an individual, but all potential properties are contiguous parts of a true continuum that exceeds all multitude.

On that note - do you agree that nominalism requires space and time (and everything else) to be discrete, rather than continuous? Otherwise, they would not consist of individual locations and moments.

I am suggesting that both of these statements are correct, but "there are" means two different things. Properties only exist in particulars, but properties are real - i.e., they have another mode of being — aletheist

What I'm trying to avoid in my last post, though, is any suggestion of what sort of ontological stuff anything is. It gets frustrating sometimes because I don't know what you'd accept as the most general term, and I don't want the conversation to devolve into haggling over "technical" definitions of "exist" versus "real" versus "there are" etc. That's why I chose "there are" because I was trying to find a term that would be neutral. Sometimes it can seem like we (not just me and you, but people on different sides of these issues in general) can't even have a conversation about this stuff in terms of logical relationships at all, because no matter what term is chosen to mention something, the response is, "Well, that doesn't 'exist'" or "That isn't 'real'" or "That isn't something there 'is'" etc.--because it turns out that the person is using some technical definition of "exist" or "real" or "there is" that doesn't include everything. (And of course, people will say, "That's not a thing," etc.)

It sounds like you'd maybe use "being" as the most general term?

If so, then what I'm asking is this: As long as we accept that properties have being and particulars that exhibit properties have being, there are only two possibilities: only properties "in" particulars have being or properties separate from particulars have being, too.

If "being" wouldn't do as the most general term for "having any sort of 'present' ontological status" (and hopefully now we won't have to haggle over "present"), then let's just use a made-up word, let's say, "ontogeneral." where we're going to use that to whatever the broadest ontological category would be that would cover anything that " <<whatevers>> (I can't choose a more specific word, or you'll haggle): So then it would be:

As long as we accept that properties have ontogeneral status and particulars that exhibit properties have ontogeneral status, there are only two logical possibilities: only properties "in" particulars have ontogeneral status or properties separate from particulars have ontogeneral status, too.

In other words, I'm only speaking about a logical relationship fact on a very abstract level. I'm not saying anything that makes any sort of ontological commitment whatsoever about what anything "really is."

So do you agree that there are only those two possibilities?

As long as we accept that properties have ontogeneral status and particulars that exhibit properties have ontogeneral status, there are only two logical possibilities: only properties "in" particulars have ontogeneral status or properties separate from particulars have ontogeneral status, too ... So do you agree that there are only those two possibilities? — Terrapin Station

I honestly have no desire to "haggle," but if "we accept that properties have ontogeneral status," are we adopting realism and rejecting nominalism? If not, I cannot understand what you mean by "ontogeneral status." As I said before, I am suggesting that properties "in" particulars are actualizations of real continua of potential properties.

What about my question - do you agree that nominalism requires space and time (and everything else) to be discrete, rather than continuous?

I honestly have no desire to "haggle," but if "we accept that properties have ontogeneral status," are we adopting realism and rejecting nominalism? — aletheist

In talking about the logical relationship I'm focusing on, I'm talking ONLY about the logical relationship, and I'm trying to avoid any ontological commitments. So by answering you're not committing yourself to any stance a la realism on universals, nominalism, etc. The point is to only focus on the logical relationship at the moment. I'm merely trying to encourage clear thinking about the logical possibilities.

The point is to only focus on the logical relationship at the moment. — Terrapin Station

The logical relationship of what, exactly? And why do I have to answer your question before you address mine?

The logical relationship of what, exactly? — aletheist

What I've been talking about. Again, it seems to me that there are only two logical possibilities (I'll give the nutshell version;)

Either

A. Properties only <<whatever>> in particulars

or

B. Properties at least partially <<whatever>> separately from particulars.

(Where (a) "<<whatever>>" is an avoidance substitute for terms like "exist," "occur," "obtain," "have being," etc., and (b) I'm not implying anything at all about just what sort of ontological <<whatever>> we're talking about.)

The logical relationship between a general property and its individual instantiations is the same as that between a truly continuous line and the discrete points that can be marked on it. Note that the line does not consist of these points, no matter how many of them are marked; rather, between any two actual points, the continuum includes potential points exceeding all multitude, all of which are also real. Likewise, a general property is not merely the collection of its individual instantiations.

Now - do you agree that nominalism requires space and time (and everything else) to be discrete, rather than continuous?

the form of the particular is the essential properties as well as all the accidentals. — Metaphysician Undercover

But my constraints approach to form would simplify this so that particular forms are simply more constrained versions of general forms. So even a particular form is "all essence". And then accidents are simply aspects of form which are a matter of indifference. They are "particulars" that don't particularly matter.

So you in fact get the largest number of possible accidentals under the most general forms. Generality can afford to be the least fussy - by inductive definition.

That is why the most general law or telos of nature - the second law of thermodynamics - winds up being the "law of the accidental". It is all about randomness and disorder.

Particular forms have to be the most particular, by contrast. A crucifix is a particular form. It can still vary a fair bit but you have to have at least two lines crossing at about a right angle.

So all form is tolerant of accidents to some degree. And particularity arises from generality by narrowing the definition of the accidental - making it also more particular. Or crisper.

I don't think this "triadic/development" is the right direction. What you propose only reinforces the designated status of matter (potential) as unintelligible. it asserts the position of the unintelligible (matter) as more fundamental than the intelligible, placing it out of reach of the intellec — Metaphysician Undercover

Yet it contradicts dialectical reasoning to not accept that there must be the unintelligible for there to be the intelligible. It can make no sense to claim the one except in the grounding presence of its other. So as soon as you commit to crisp intelligibility, you are committed to its dichotomous other - vague unintelligibility - as a necessity.

And that's great because it explains the mysterious nature of matter as naked potential. Material cause ends up being complete, yet undirected, action. Just limitless fluctuation. Then material cause becomes efficient cause when it's chaotic dynanism becomes directed, or in-formed.

Efficient cause thus is the material cause made substantial - concrete and crisp in its identity. Now it is transformed into the kind of static stuff that reliably does things.

Likewise, we have the same move from final to formal cause. Finality is a pure action principle - a vague desire. It may be all direction, in contrast to material cause, but it lacks any means as yet. Finality needs to be cashed out in the shape of some formal cause, some organised and enduring and anti-chaotic structure.

So the deepest causes - the material potential and the telic potential - are both active or dynamical. Then they cash out as static enduring substantial actuality by resulting in in-formed matter (efficient cause) and en-mattered purpose (formal cause).

This will bring matter (potential) out from the designation of vagueness, the apeiron, into the category of intelligible. — Metaphysician Undercover

But you need vagueness to make its inverse an intelligible possibility. The difficulty is then to represent this in some fundamental metaphysical framework.

I've just accounted for it with the familiar four causes organicism of Aristotle. Peirce offers an even more compact representation in his triadic sign relation, or semiotic.

Now in this view we have the three things of vague potential, definite reaction, and constraining habit. You get an actual developmental account of how substantial being occurs.

But it is very densely packed. And it requires familiarity with the new category of the vague~crisp, as well as an understanding of formal and final cause as constraints in a system, not constructive degrees of freedom.

And I should add that Peirce also brings in yet another foundational dichotomy in terms of matter~sign. So at the level of substantial actuality, he discovers the difference that divides the realms of the physical and the mental, the real and the fictive, the entropic and the negentropic.

It is all a bunch of dichotomies. And a triadic metaphysics is the only way to "rotate" them so they map to each other in a completely self consistent fashion.

The logical relationship between a general property and its individual instantiations is the same as that between a truly continuous line and the discrete points that can be marked on it. Note that the line does not consist of these points, no matter how many of them are marked; rather, between any two actual points, the continuum includes potential points exceeding all multitude, all of which are also real. Likewise, a general property is not merely the collection of its individual instantiations. — aletheist

You're not really addressing what I asked you though. Do you see this as a third possibility between properties only in particulars and properties that are also separate? Aren't the potential points separate from the actual points?

Re this, by the way:

Now - do you agree that nominalism requires space and time (and everything else) to be discrete, rather than continuous? — aletheist

No--I don't think it would make any difference if space and time were discrete rather than continuous. However, I won't discuss this any further if we don't finish the other thing first.

No--I don't think it would make any difference if space and time were discrete rather than continuous. — Terrapin Station

Being unconstrained by any demand for consistency, one can indeed claim to believe anything.

One could believe anything constrained by demands for consistency, too. Not everyone has the same views on what's consistent, and folks can rationalize any conceivable belief.

Aren't the potential points separate from the actual points? — Terrapin Station

No, the potential points are continuous with the actual points. That is why I had such a hard time with both of the options that you presented. However, any two actual points are "separate" from each other in the sense that there are potential points exceeding all multitude between them.

No--I don't think it would make any difference if space and time were discrete rather than continuous. — Terrapin Station

If space and time are truly continuous, then they exceed all multitude of individual locations and instants. But nominalism holds that only individuals exist, and only that which exists is real; hence it entails that if space and time exist and are real, then they must be discrete, consisting of distinct individual locations and instants.

No, the potential points are continuous with the actual points. — aletheist

Ah--I'm not meaning separate as in "disconnected" or "having nothing to do with" or something like that. I mean that either they're the same in every respect, including numerically, to the actual points or they're not the same in every respect, including numerically. "Not the same in every respect" is what I'm using the word "separate" for. You're not saying that the potential points are the same in every respect to the actual points, are you--otherwise what the heck is the potential/actual distinction? If that doesn't peg some difference, the distinction would make no sense.

One could believe anything constrained by demands for consistency, too. — Terrapin Station

And if one's beliefs are constrained by empirical correspondence AND rational coherence, then one has truly arrived at the pragmatist's nirvana of it getting as it good as it gets.

Not everyone has the same views on what's consistent, and folks can rationalize any conceivable belief. — Terrapin Station

Yep. You need empirical test too. But logical coherence is a good place to start.

It seems to me that the whole concept of numerical identity only applies to determinate individuals. Hence we can say that no two actual points on a truly continuous line are numerically identical, but it makes no sense even to ask whether an actual point is numerically identical to any potential (i.e., indeterminate) point on the same line, or whether two "adjacent" potential points are numerically identical. The latter are contiguous, and therefore indistinguishable, yet potentially different; the laws of non-contradiction and excluded middle do not apply unless and until individuals are actualized.

whether two "adjacent" potential points are numerically identical. — aletheist

So you'd maybe say that two adjacent points are numerically the same?

No, there is nothing "numerical" about potential points on a truly continuous line. Every part of a true continuum is itself a true continuum. Between any two "adjacent" potential points, there are potential points that exceed all multitude.

You'd say there can be two adjacent points?